ric: parameter-free noise-robust clustering

Intelligent Database Systems Lab

國立雲林科技大學National Yunlin University of Science and Technology

RIC: Parameter-Free Noise-Robust Clustering

Presenter : Shu-Ya Li

Authors : CHRISTIAN BO¨ HM, CHRISTOS FALOUTSOS,

JIA-YU PAN, CLAUDIA PLANT

TKDD, 2007

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I. M.Outline

Motivation

Objective

Methodology

Experiments and Results

Conclusion

Personal Comments

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I. M.Motivation

How to find a natural clustering of a real-world point set which contains

an unknown number of clusters with different shapes

the clusters may be contaminated by noise?

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I. M.Objectives

Find natural clustering in a dataset Goodness of a clustering

We use Volume after Compression (VAC) to quantify the ‘goodness’ of a grouping by.

Efficient algorithm for good clustering

Robust Fitting Cluster Merging

MDL for classificationVAC for clustering

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I. M.VAC (Volume after Compression )

VAC Tells which grouping is better

Lower VAC => better grouping

Formula using decorrelation matrix

Computing VAC Compute covariance matrix of cluster C

Compute PCA and obtain decorrelation matrix

Compute VAC from the matrix

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I. M.Computing VAC

VAC (volume after compression) Record bytes to record their type (guassian, uniform,..)

Record bytes for number of clusters k

The bytes to describe the parameters of each distribution (e.g., mean, variance, covariance, slope, intercept) and then the location of each point

Cluster Model

stat = (μi, σi, lbi, ubi, ...)

2.3+4.3=6.6bits

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I. M.Methodology – RIC framework

Robust Fitting Mahalanobis distance defined by Λ and V

Conventional estimation: covariance matrix uses Mean

Robust estimation: covariance matrix uses Median

Median is less affected by outliers than Mean

PCA (Σ = V ΛV T)

median

μ

μR

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I. M.Methodology – RIC framework

Cluster Merging Merge Ci and Cj only if the combined VAC decreases

If savedCost > 0, then merge Ci and Cj

Greedy search to maximize savedCost, hence minimize VAC

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I. M.Experiments

Results on Synthetic Data

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I. M.Experiments

Performance on Real Data

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I. M.Experiments

Compares the result of filterOpt to the result of filterDist.

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I. M.Conclusion

The contributions of this work are the answers to the two questions, organized in our RIC framework. (Q1) Goodness Measure.

We propose the VAC criterion using information-theory concepts, and specifically the volume after compression.

(Q2) Efficiency. Robust fitting (RF) algorithm, which carefully avoids outliers.

Cluster merging (CM) algorithm, which stitches clusters together if the stitching gives a better VAC score.

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I. M.Personal Comments

Advantage Description detail

Many pictures and examples

Drawback It is difficult to identify black and white picture.

Application Clustering